Department of Physics, Vijayanagar College, Hospet-583201, India.
E-mail: umapati.pattar@gmail.com
(Received 26 June 2014, accepted 13 December 2014)
Abstract
Determination of dielectric constant of a solid involves the measurement of capacitance of the capacitor with dielectric material, if one knows the physical dimensions. The simpler and easier to measure the dimensions of a capacitor is that of a parallel plate capacitor. Here we use commercially available alluminium panel sheet (APS), where the low density polyethylene (LDPE) is laminated using two thin alluminium sheets, which acts as a dielectric material. The capacitances of the different dimensions of the APS are measured and hence the dielectric constant of the LDPE is determined. We measured the time constant from charging curve by applying square waves using a cathode ray oscilloscope (CRO) and hence determined the capacitance. By measuring the dimensions of the samples the dielectric constant was calculated. Low cost, simplicity, and accuracy are the features of this experiment.
Keywords: Capacitance, Dielectric constant, time constant, charging and discharging.
Resumen
La determinación de la constante dieléctrica de un sólido implica la medición de la capacitancia del condensador con material dieléctrico, si se conocen las dimensiones físicas. El tipo de condensador más simple y fácil de medir en sus dimensiones, es el condensador de placas paralelas. Se utilizó panel de hoja de aluminio (APS) disponible comercialmente, en el que el polietileno de baja densidad (LDPE) se lamina usando dos hojas delgadas de aluminio que actúan como un material dieléctrico. Las capacitancias de los APS de diferentes dimensiones se miden, y consecuentemente se determina la constante dieléctrica del LDPE. Se midió la constante de tiempo de la curva de carga al aplicar ondas cuadradas utilizando un osciloscopio de rayos catódicos (CRO), y con ello se determinó la capacitancia. Midiendo las dimensiones de las muestras, se calculó la constante dieléctrica. Bajo costo, sencillez y precisión son las características de este experimento.
Palabras clave: Capacitancia, constante dieléctrica, constante de tiempo, carga y descarga.
PACS: 78.20 Ci, 84.37. +q, 84.32.Tt ISSN 1870-9095
determined by measuring the dimensions of the samples.
The method of experimentation not only yielded accurate
The concept of capacitance involves the understanding of concentration of electric field between the two plates of a capacitor, which depends on the dielectric material between the plates of a capacitor. The relation which connects the character of the dielectric material (called dielectric constant, 𝜀
ε r
ε
0
!
A
) with the capacitance is a simple, i.e.
C = . Hence several experiments are being done to d determine the dielectric constant of a solid dielectric [1, 2, result but also proved to be more effective in conveying the concept of variation of capacitance with area. This method was tried by other teachers of our University, and has been adopted in the colleges.
According to Coulomb’s law, the force between two
3, 4, 5, 6, 7, 8, 9, 10].
Most of these use thin sheet/s of paper as the dielectric material. The use of paper sheets introduces air gaps which affect the accuracy of the result to a larger extent. When charges is given by the equation: this was discussed with the students, some of the students suggested the use of commercially available Alluminium
Panel Sheet (APS) as capacitor and determine the dielectric constant of low density polyethylene (LDPE) which was laminated using two thin sheets of Alluminium. The capacitances of different dimensions of the APS are measured and hence the dielectric constant of the LDPE is
F = C q
1 q r 2
2
. (1)
The equation has the identical form as Newton’s law of gravitation and the constant C is analogous to the gravitational constant which determines the force between two masses. The dielectric constant ε
0 related to C by:
measured here is
Lat. Am. J. Phys. Educ. Vol. 8, No. 4, Dec. 2014 4318-1 http://www.lajpe.org

Umapati Pattar
C =
1
4
0
. (2)
A parallel plate capacitor consists of two parallel conducting plates. If we move an electric charge Q from one plate to the other at a potential Δ V , the capacitance of the pair may be calculated using the equation:
C =
Q
V
. (3)
The electric field which exists between the plates is simply:
E =
V d
. (4)
Where d is the distance between the plates. If the surface charge density is σ , then Gauss’s law says the potential difference and electric field between the plates is:
V = Ed =
d
0
. (5)
If the plate area is A , then the total charge on the plate is
Q= σ A . The plate capacitance is now:
C =
Q
Δ V
=
d
A
0
=
0
A d . (6)
If the medium between the two plates is something besides free space, then it is necessary to replace ε
0
with the dielectric constant of the material. Usually this is expressed using the term relative dielectric,
ε r
=
ε
ε
0 where ε is the dielectric constant of the material and ε r
is its relative dielectric value. The relative dielectric is therefore a unit less number usually in the range of 1 to 20.
The capacitance with a dielectric medium of dielectric constant ε r
will then be:
C =
r
d
0
A
. (7)
Commercially available capacitors are either cylindrical or disc type. In both the cases, it is not possible to study variation of capacitance with distance between the plates or determine the dimensions; area and distance between the plates, in order to calculate the dielectric constant of the medium. Here we use commercially available aluminium panel sheets 1 of different sizes as capacitors. By measuring the areas and noting the distance between the aluminium
1
These sheets are used for exterior decoration, wall cladding etc. and available in different sizes and thicknesses. We used Eurobond 3mm thick sheet. The thickness of alluminium foil was 0.25mm and thickness of
LDPE core was 2.5mm.
Lat. Am. J. Phys. Educ. Vol.8, No. 4, Dec. 2014r 4318-2 sheets from the data available from the manufacturer, we can determine the dielectric constant of the material (which is low density poly ethylene, LDPE) if we determine the capacitance C between the aluminium sheets and core
(LDPE).
The capacitances of theses sheets are very small; of the order of nano-farad; it is difficult to record voltages at different intervals unless we have a resistor of Giga (10
9
)
Ohm.
Hence we apply square wave of suitable frequency and measure the time constant from the charging curve using an oscilloscope. If we apply a continuous square wave voltage waveform to the RC circuit whose frequency matches exactly to that of the 5 RC time constant (5 T ) of the circuit, then the charging voltage waveform across the capacitor would look as in Figure 1.
FIGURE 1. The voltage drop across the capacitor alternates between charging up to V
C
and discharging down to zero according to the input voltage. Here the frequency (and therefore the time period, ƒ = 1/ T ) of the input square wave voltage approximately matches that of the 5 times RC time constant, ƒ =
1/5 RC , and the capacitor is allowed to fully charge and fully discharge on every cycle resulting in a perfectly matched RC waveform.
Ø Arrange the experimental setup as shown in Figure 2.
FIGURE 2. Description of capacitor connection to a SQR wave generator and the oscilloscope.
Ø Connect the Square wave generator alone to the oscilloscope and Set the Square wave voltage 𝑉
!
!
!
20 volts.
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Ø Make the connections as shown in Figure 2.
Ø Keep the frequency of Square wave a constant value
(Between 6 to 8 KHz). Adjust resistance and time per division control on the oscilloscope, so that a clear and minimum one complete cycle of charging curve is displayed on the oscilloscope.
Ø Using X-shift control of the oscilloscope move the charging curve along the X-axis until the charging curve meets the 12.6
V (which is 63% of the Square wave voltage) point on the Y-axis of the oscilloscope as shown in Figure 3.
Ø Note the number of horizontal divisions the charging curve has been moved.
Ø Calculate the time constant by multiplying with time per division on the CRO.
Ø Repeat the above steps for plates of different areas
Ø Dielectric constant is calculated using slope of the
Ø straight line(Figure 3) from the formula: 𝜀
!
=
!
!
!
× 𝑆𝑙𝑜𝑝𝑒 . (8)
The thickness of the APS is a standard one, can easily be found from the supplier or from technical data provided (we used 2.5mm thick sheet).
An innovative approach to determine the dielectric constant of a solid being well sealed and surfaces painted reduce these errors to a considerable extent. Somewhat subjectivity is introduced in the measurement of time constant from the charging curve; this can further be reduced using high quality L-C-R bridge capacitance meter. Where C is directly measured.
FIGURE 3. Wave shape detected in the oscilloscope.
Typical value of dielectric constant of low density polyethylene ranges from 2.2 to 2.35.
The physical dimensions of commercially available capacitors, either parallel plate or cylindrical, being too small for the measurements, hence the difficulty of determining the value of dielectric constant. Many experiments have been done using two bigger metal plates and paper sheet or glass sheet as dielectric media, but the air gaps introduces the considerable error [11]. The APS
FIGURE 4. Graph of capacitance vs.
area of the plates.
[1] Parker, G. W., Electric field outside a parallel plate capacitor, Am. J. Phys. 70 , 502–507 (2002).
[2] Kraftmakher, Y., Measurement of dielectric constant of gases, Am. J. Phys. 64 , 1209–1210 (1996).
[3] Meyer, J. J. and Behof, A. F., Experiment on the motion of a dielectric in a parallel plate capacitor, Am. J. Phys.
62 , 931 (1994).
[4] Carlson, G. T. and Illman, B. L., The circular disk parallel plate capacitor, Am. J. Phys. 62 , 1099–1105
(1994).
[5] Yan, F. N. and Wong, H. K., Force between the plates of a parallel-plate capacitor, Am. J. Phys. 61 , 1153 (1993).
[6] Wilson, D. E., A direct laboratory approach to the study of capacitors, Am. J. Phys. 57 , 630–632 (1989).
[7] Utreras-Diaz, C. A., Dielectric slab in a parallel plate capacitor, Am. J. Phys. 56 , 700–701 (1988).
[8] Harwood, R. J. and Kinkaid, D. E., Use of a Mettler balance and a parallel plate capacitor to measure the permittivity of free space, Am. J. Phys. 43 , 924–925 (1975).
[9] Karlow, E. A., Let’s measure the dielectric constant of a piece of paper!, Phys. Teach. 29 , 23–25 (1991).
[10] Foong, S. K. and Lim, C. H., On the capacitance of a rolled capacitor, Phys. Educ. 37 , 429–430 (2002).
[11] Grove, T. T., Masters, M. F. and Miers, R. E.,
Determining dielectric constants using a parallel plate capacitor , Am. J. Phys. 73 , 52-56 (2005).
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